Find the greatest common factor of $6$ and $35$.
The greatest common factor (GCF) is the largest number that is a factor of both $6$ and $35$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}6 &=2\cdot3\\\\\\\\ 35&=5\cdot7 \end{aligned}$ Since these numbers have no common prime factors, we say that the GCF is $1$. This is because all numbers share a factor of $1$ : $ \begin{aligned}6 &=2\cdot3\cdot1\\\\\\\\ 35&=5\cdot7\cdot1 \end{aligned}$ The greatest common factor of $6$ and $35$ is $1$.